多层前向小世界神经网络及其函数逼近

借鉴复杂网络的研究成果, 探讨一种在结构上处于规则和随机连接型神经网络之间的网络模型—-多层前向小世界神经网络. 首先对多层前向规则神经网络中的连接依重连概率p进行重连, 构建新的网络模型, 对其特征参数的分析表明, 当0 < p < 1时, 该网络在聚类系数上不同于Watts-Strogatz 模型; 其次用六元组模型对网络进行描述; 最后, 将不同p值下的小世界神经网络用于函数逼近, 仿真结果表明, 当p = 0:1时, 网络具有最优的逼近性能, 收敛性能对比试验也表明, 此时网络在收敛性能、逼近速度等指标上要优于同规模的规则网络和随机网络.     

基于SIR模型的时间侵占行为传播动力学建模与仿真

针对时间侵占行为在复杂网络上的传播问题,基于基本SIR传染病模型,提出了一种考虑了自发感染率和外部组织环境因素的时间侵占行为传播模型,探讨了时间侵占行为在ER随机网络,NW小世界网络,WS小世界网络以及BA无标度网络上的传播,在此基础上,集中分析了无标度网络上时间侵占行为传播的影响因素。研究发现:1. 时间侵占行为的传播受压力和公平系数的影响,一定范围内,压力越小,员工发生时间侵占行为的概率越大,传播过程也越快;反之压力越大,发生时间侵占行为的概率越小,传播过程也相对较为缓慢。2.时间侵占行为的传播与传播概率和自发感染概率密切相关,初始节点的度越大,传播越快,反之传播越慢。     

Controlling the spreading in small-world evolving networks: stability, oscillation, and topology

The spreading of viruses, diseases, and even disasters (such as power blackouts and financial crises) in many large-scale and small-world networks is one of the mostly concerned issues today. In this note, we study general spreading dynamical behaviors in small-world evolving networks when control strategies are applied to suppress the propagation of diseases, viruses, and disasters. After proposing a novel Watts-Strogatz (W-S) spreading model to capture the general spreading mechanism in small-world networks, we investigate the stability and Hopf bifurcations of delay-controlled spreading models with linear and nonlinear feedback controllers, where parameters of small-world rewiring probability, feedback control gain, and time delay are analyzed for the oscillating behaviors. We conclude that the oscillatory spreading phenomena in delay-controlled small-world networks are topologically inherent.     

On the emergence of chaos in dynamical networks

We investigate how changes of specific topological features result on transitions among different bounded behaviours in dynamical networks. In particular, we focus on networks with identical dynamical systems, synchronised to a common equilibrium point, then a transition into chaotic behaviour is observed as the number of nodes and the strength of their coupling changes. We analyse the network's transverse Lyapunov exponents (tLes) to derive conditions for the emergence of bounded complex behaviour on different basic network models. We find that, for networks with a given number of nodes, chaotic behaviour emerges when the coupling strength is within a specific bounded interval; this interval is reduced as the number of nodes increases. Furthermore, the endpoints the emergence interval depend on the coupling structure of network. We also find that networks with homogeneous connectivity, such as regular lattices and small-world networks are more conducive to the emergence of chaos than networks with heterogeneous connectivity like scale-free and star-connected graphs. Our results are illustrated with numerical simulations of the chaotic benchmark Lorenz systems, and to underline their potential applicability to real-world systems, our results are used to establish conditions for the chaotic activation of a network of electrically coupled pancreatic β-cell models.     

Robustness of regular ring lattices based on natural connectivity

It has been recently proposed that natural connectivity can be used to efficiently characterise the robustness of complex networks. The natural connectivity quantifies the redundancy of alternative routes in the network by evaluating the weighted number of closed walks of all lengths and can be seen as an average eigenvalue obtained from the graph spectrum. In this article, we explore both analytically and numerically the natural connectivity of regular ring lattices and regular random graphs obtained through degree-preserving random rewirings from regular ring lattices. We reformulate the natural connectivity of regular ring lattices in terms of generalised Bessel functions and show that the natural connectivity of regular ring lattices is independent of network size and increases with K monotonically. We also show that random regular graphs have lower natural connectivity, and are thus less robust, than regular ring lattices.     

一种动态的移动社交网络拓扑模型

针对移动社交网络的动态性、用户不同重要性和信息交互有向性,基于4种初始网络提出能准确描述移动社交网络结构的拓扑模型。采用随机游走理论和改进的PageRank算法,引入过渡概率使每两时步之间的网络拓扑结构相互联系。通过PageRank算法得到节点的势,进而求出概率过渡矩阵,利用随机游走理论由上一时步边存在概率矩阵和概率过渡矩阵得到当前时步边存在概率矩阵,每一时步动态地增加一个节点并检验是否有离开的节点。仿真结果显示,该模型在4种初始网络下得到的网络拓扑结构,入度、出度、势分布以及度-势相关性均具有明显幂律特性,表明随机游走理论和改进的PageRank算法能较准确描述移动社交网络,具有一定的实践意义。     

节点传播能力的偏好随机行走的信息传播方法

随机行走是社交和生物系统中用来模拟传播过程的标准化工具,针对真实社交网络中任意程度的有偏随机行走过程和由优先转移概率定义的偏向性,提出了一种新的用于研究社交网络的影响力传播范围最大化的方法,称之为基于节点传播能力的偏向性随机行走的网络信息传播方法（DCID）,该方法随机从网络中选择一个信息传播源节点,使得该模型更加符合真实的社交网络;通过节点能承受的传播信息的内容量参数以及偏向性随机行走的参数来作为节点的优先转移概率;并通过影响力传播函数来衡量信息的影响力传播范围,以此达到信息传播范围的最大化。从真实的不同规模的社交网络中选定这两个参数值,并验证了提出的模型在不同规模社交网络中信息的覆盖率和算法运行时间的性能上有所提升。     

Software execution processes as an evolving complex network

Inspired by the surprising discovery of several recurring structures in various complex networks, in recent years a number of related works treated software systems as a complex network and found that software systems might expose the small-world effects and follow scale-free degree distributions. Different from the research perspectives adopted in these works, the work presented in this paper treats software execution processes as an evolving complex network for the first time. The concept of software mirror graph is introduced as a new model of complex networks to incorporate the dynamic information of software behavior. The experimentation paradigm with statistical repeatability was applied to three distinct subject programs to conduct several software experiments. The corresponding experimental results are analyzed by treating the software execution processes as an evolving directed topological graph as well as an evolving software mirror graph. This results in several new findings. While the software execution processes may demonstrate as a small-world complex network in the topological sense, they no longer expose the small-world effects in the temporal sense. Further, the degree distributions of the software execution processes may follow a power law. However, they may also follow an exponential function or a piecewise power law.     

基于稀疏贝叶斯算法的演化博弈网络重构

演化博弈是自然和社会系统中一种常见的互动类型,探知演化博弈网络的拓扑结构是理解其功能和集体行为的基础。对于演化博弈网络,个体的博弈行为通常难以用动力学方程进行描述,而且相关的时序信息一般数量有限并且是离散的,因此在有限的个体博弈信息下重构网络的结构有着重要的研究意义。本文基于稀疏贝叶斯学习方法进一步发展了演化博弈网络的重构方法,通过在随机网络和小世界网络上的数值模拟验证该方法的有效性。与先前的基于L1范数的方法相比,该方法同样能够在较少的个体博弈信息下实现网络的重构,并且具有更高的重构效率和更强的噪声鲁棒性。     

Ultrafast vectorized multispin coding algorithm for the Monte Carlo simulation of the 3D Ising model

A new Monte Carlo algorithm for the 3D Ising model and its implementation on a CDC CYBER 205 is presented. This approach is applicable to lattices with sizes between 3·3·3 and 192·192·192 with periodic boundary conditions, and is adjustable to various kinetic models. It simulates a canonical ensemble at given temperature generating a new random number for each spin flip. For the Metropolis transition probability the speed is 27 ns per updates on a two-pipe CDC Cyber 205 with 2 million words physical memory, i.e. 1.35 times the cycle time per update or 38 million updates per second.     

Functional Topology Classification of Biological Computing Networks

Current analyses of complex biological networks focus either on their global statistical connectivity properties (e.g. topological path lengths and nodes connectivity ranks) or the statistics of specific local connectivity circuits (motifs). Here we present a different approach – Functional Topology, to enable identification of hidden topological and geometrical fingerprints of biological computing networks that afford their functioning – the form-function fingerprints. To do so we represent the network structure in terms of three matrices: 1. Topological connectivity matrix – each row (i) is the shortest topological path lengths of node i with all other nodes; 2. Topological correlation matrix – the element (i,j) is the correlation between the topological connectivity of nodes (i) and (j); and 3. Weighted graph matrix – in this case the links represent the conductance between nodes that can be simply one over the geometrical length, the synaptic strengths in case of neural networks or other quantity that represents the strengths of the connections. Various methods (e.g. clustering algorithms, random matrix theory, eigenvalues spectrum etc.), can be used to analyze these matrices, here we use the newly developed functional holography approach which is based on clustering of the matrices following their collective normalization. We illustrate the approach by analyzing networks of different topological and geometrical properties: 1. Artificial networks, including – random, regular 4-fold and 5-fold lattice and a tree-like structure; 2. Cultured neural networks: A single network and a network composed of three linked sub-networks; and 3. Model neural network composed of two overlapping sub-networks. Using these special networks, we demonstrate the method’s ability to reveal functional topology features of the networks.     

神经元网络场电位的迭代学习控制研究

基于映射神经元模型和Hindmarsh-Rose神经元模型构建小世界神经网络,并施加带有遗忘因子的迭代学习控制算法,以实现神经网络的同步控制。仿真结果表明迭代学习控制同时适用于离散的和连续的神经网络模型,可以实现神经网络同步和去同步状态的相互转化,其优势在于随着迭代次数的增加,控制信号强度逐渐减弱,从而保持神经元本身的放电特性不变。所得结果为将非线性控制理论应用于帕金森等神经疾病控制提供了新思路。     

SmallWorld Model-Based Polylogarithmic Routing Using Mobile Nodes

The use of mobile nodes to improve network system performance has drawn considerable attention recently. The movement-assisted model considers mobility as a desirable feature,where routing is based on the store-carry-forward paradigm with random or controlled movement of resource rich mobile nodes.The application of such a model has been used in several emerging networks,including mobile ad hoc networks(MANETs),wireless sensor networks(WSNs),and delay tolerant networks(DTNs).It is well known that mobility increases the capacity of MANETs by reducing the number of relays for routing,prolonging the lifespan of WSNs by using mobile nodes in place of bottleneck static sensors,and ensuring network connectivity in DTNs using mobile nodes to connect different parts of a disconnected network.Trajectory planning and the coordination of mobile nodes are two important design issues aiming to optimize or balance several measures, including delay,average number of relays,and moving distance.In this paper,we propose a new controlled mobility model with an expected polylogarithmic number of relays to achieve a good balance among several contradictory goals,including delay,the number of relays,and moving distance.The model is based on the small-world model where each static node has"short"link connections to its nearest neighbors and"long"link connections to other nodes following a certain probability distribution.Short links are regular wireless connections whereas long links are implemented using mobile nodes.Various issues are considered,including trade-offs between delay and average number of relays,selection of the number of mobile nodes,and selection of the number of long links.The effectiveness of the proposed model is evaluated analytically as well as through simulation.     

Modeling and Simulation Study of the Propagation and Defense of Internet E-mail Worms

As many people rely on e-mail communications for business and everyday life, Internet e-mail worms constitute one of the major security threats for our society. Unlike scanning worms such as Code Red or Slammer, e-mail worms spread over a logical network defined by e-mail address relationships, making traditional epidemic models invalid for modeling the propagation of e-mail worms. In addition, we show that the topological epidemic models presented by M. Boguna, et al. (2000) largely overestimate epidemic spreading speed in topological networks due to their implicit homogeneous mixing assumption. For this reason, we rely on simulations to study e-mail worm propagation in this paper. We present an e-mail worm simulation model that accounts for the behaviors of e-mail users, including e-mail checking time and the probability of opening an e-mail attachment. Our observations of e-mail lists suggest that an Internet e-mail network follows a heavy-tailed distribution in terms of node degrees, and we model it as a power-law network. To study the topological impact, we compare e-mail worm propagation on power-law topology with worm propagation on two other topologies: small-world topology and random-graph topology. The impact of the power-law topology on the spread of e-mail worms is mixed: E-mail worms spread more quickly on a power-law topology than on a small-world topology or a random-graph topology, but immunization defense is more effective on a power-law topology.     

SIS model of epidemic spreading on dynamical networks with community

We present a new epidemic Susceptible-Infected-Susceptible (SIS) model to investigate the spreading behavior on networks with dynamical topology and community structure. Individuals in themodel are mobile agentswho are allowed to perform the inter-community (i.e., long-range) motion with the probability p. The mean-field theory is utilized to derive the critical threshold (λ _C ) of epidemic spreading inside separate communities and the influence of the long-range motion on the epidemic spreading. The results indicate that λ _C is only related with the population density within the community, and the long-range motion will make the original disease-free community become the endemic state. Large-scale numerical simulations also demonstrate the theoretical approximations based on our new epidemic model. The current model and analysis will help us to further understand the propagation behavior of real epidemics taking place on social networks.     

带恢复策略的复杂网络级联失效机理及鲁棒性研究

为研究复杂网络在遭遇随机故障或蓄意攻击时的鲁棒性,考虑节点具有恢复和重复失效等特征,构建故障节点概率传播模式下的级联失效模型.构建节点故障概率随故障次数增加而逐渐降低的故障概率函数,设计概率恢复(R)和阶段恢复(T)两种故障节点恢复策略,并针对ER、WS、NC和BA四类网络研究其恢复鲁棒性.仿真实验考虑模型中相关参数变化,揭示其对复杂网络级联失效过程中的鲁棒性影响,综合分析边鲁棒性和节点鲁棒性的性能权衡.仿真结果表明,在概率恢复策略下,随着恢复率的增大,4类网络级联失效的规模均能够实现有效降低;而在阶段恢复策略下,随着参数T值增加到不同阈值,4类网络鲁棒性指标在级联失效过程中均能够呈现出突变现象.     

基于在线社交网络的动态消息传播模型

传统传播模型较难描述在线社交网络中的复杂活跃模式以及节点间的拓扑差异,并且其接触式的传播者退化方式也与现实不符。针对理论模型模拟与现实消息传播的不符,提出一个基于在线社交网络的动态消息传播模型D-SIR。该模型考虑了在线社交网络中影响消息传播的一些实际因素,引入基于传播延迟的退化方式使传播者自发地退化成免疫者,动态指定节点的权威度和免疫力以适应非均质网络,并考虑接收增强信号效应以及外部社会加强效果。在采集的新浪微博真实传播网络数据中,通过参数变化的传播仿真实验验证了D-SIR模型可以有效反映在线社交网络的现实传播情形,并且较传统模型更具灵活性及可扩展性。     

Structure versus function: a topological perspective on immune networks

Many recent advances have been made in understanding the functional implications of the global topological properties of biological networks through the application of complex network theory, particularly in the area of small-world and scale-free topologies. Computational studies which attempt to understand the structure–function relationship usually proceed by defining a representation of cells and an affinity measure to describe their interactions. We show that this necessarily restricts the topology of the networks that can arise—furthermore, we show that although simple topologies can be produced via representation and affinity measures common in the literature, it is unclear how to select measures which result in complex topologies, for example, exhibiting scale-free functionality. In this paper, we introduce the concept of the potential network as a method in which abstract network topologies can be directly studied, bypassing any definition of shape-space and affinity function. We illustrate the benefit of the approach by studying the evolution of idiotypic networks on a selection of scale-free and regular topologies, finding that a key immunological property—tolerance—is promoted by bi-partite and heterogeneous topologies. The approach, however, is applicable to the study of any network and thus has implications for both immunology and artificial immune systems.     

无线网络中的一种基于小世界模型的路由协议

最近,利用节点的移动性提升网络系统性能的方法引起了不少关注。这些方法已经被运用于包括移动Adhoc网络（MANET）、无线传感网络（WSN）和容忍延时网络（DTN）在内的一些新兴网络中,他们都认为节点是随机或者可控移动的。为了达到优化或平衡包括延时、平均中继节点数目和移动距离在内的一些度量参数的目的,本文提出了一种基于于小世界模型的路由协议（SWR）。通过分析,该协议只有多对数数量级的中继节点,大大减少了报文传输过程中中继节点的数量。文中定义了短链接与长链接的概念,其中每一节点与其最邻近的节点之间存在“短”链接,而与其他遵循桌一概率分布的节点间存在着“长”链接。短链接通常是无线链接,而长链接通常是利用移动节点来实现的。本文在网络规模、使用数据搭乘者、多重长链接和等待移动节点时间方面进行了分析。通过仿真结果,我们对各方面性能进行了评估。     

A random walk model for infection on graphs: spread of epidemics &; rumours with mobile agents

We address the question of understanding the effect of the underlying network topology on the spread of a virus and the dissemination of information when users are mobile performing independent random walks on a graph. To this end, we propose a simple model of infection that enables to study the coincidence time of two random walkers on an arbitrary graph. By studying the coincidence time of a susceptible and an infected individual both moving in the graph we obtain estimates of the infection probability. The main result of this paper is to pinpoint the impact of the network topology on the infection probability. More precisely, we prove that for homogeneous graphs including regular graphs and the classical Erdős–Rényi model, the coincidence time is inversely proportional to the number of nodes in the graph. We then study the model on power-law graphs, that exhibit heterogeneous connectivity patterns, and show the existence of a phase transition for the coincidence time depending on the parameter of the power-law of the degree distribution. We finally undertake a preliminary analysis for the case with k random walkers and provide upper bounds on the convergence time for both the complete graph and regular graphs.